Preconditioning eigenvalues and some comparison of solvers

Preconditioning techniques are discussed for symmetric eigenvalue problems. The methods Davidson, Jacobi–Davidson, Rayleigh quotient iteration, and preconditioned Lanczos are considered. Some relationships are given between these different approaches, and some experimental comparisons are done. Jacobi–Davidson appears to be efficient in both expense and storage. A hybrid method may be helpful for the case of a poor initial vector.